Archibald scored his third goal in his past five games 7:12 into the second period to give the Coyotes a 1-0 lead.
"We worked hard tonight," Coyotes coach Rick Tocchet said. "We could have been up about 5-0 after the second, but give Edmonton credit, they stuck with it."
Adam Larsson scored on point shot through a screen in front at 3:27 of the third period to tie it 1-1.
"This is six of the last seven games we've played awfully well," Oilers coach Ken Hitchcock said. "We had a little bit of a soft second period, we lost a lot of face-offs and ended up defending a lot. But this is now six of seven games where we've worked really hard and competed at a high level."
The Oilers had a two-man advantage for 1:15 starting at 6:57, but were unable to capitalize.
Hinostroza scored at 10:37 when he took a pass from Niklas Hjalmarsson and scored on a backhand to give the Coyotes a 2-1 lead.
"All our [penalty] killers did a great job, whether it was 5-on-4 or 5-on-3," Hinostroza said. "Killing that 5-on-3 was huge. Whenever you can kill one of those, you give yourself a chance to win the game."
Nugent-Hopkins tied it at 19:49 on a scramble in front after he took a pass from Leon Draisaitl, who had two assists.